REVIEW Physical Principles of Nanoparticle Cellular Endocytosis

Sulin Zhang,†,‡,* Huajian Gao,§,* and Gang Bao ,) *

†Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States, ‡Department of Biomedical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States, §School of Engineering,

Brown University, Providence, Rhode Island 02912, United States, and Department) of Bioengineering, Rice University, Houston, Texas 77005, United States

ABSTRACT This review article focuses on the physiochemical mechanisms underlying nanoparticle uptake into cells. When nanoparticles are in close vicinity to a cell, the interactions between the nanoparticles and the cell membrane generate forces from different origins. This leads to the membrane wrapping of the nanoparticles followed by cellular uptake. This article discusses how the kinetics, energetics, and forces are related to these interactions and dependent on the size, shape, and stiffness of nanoparticles, the biomechanical properties of the cell membrane, as well as the local environment of the cells. The discussed fundamental principles of the physiochemical causes for nanoparticlecell interaction may guide new studies of nanoparticle endocytosis and lead to better strategies to design nanoparticle-based approaches for biomedical applications.

KEYWORDS: nanoparticles . endocytosis . nanomedicine . cellular uptake . ligandreceptor binding . coarse-grained model . membrane bending . membrane tension

he past decade has witnessed enormous for the biophysics of NPs entry into the cells research efforts undertaken in the de- via endocytosis. The theoretical focus Tvelopment of nanosized particulate renders this review distinctive from and platforms for biological studies, early stage complementary to several existing reviews cancer detection, simultaneous diagnosis on similar topics that are primarily focused and treatment of pathological conditions, on either the novel concepts and experi- and targeted therapy with minimal toxicity mental observations1315 or computational to achieve “personalized” medicine.112 To simulations.16 It also significantly extends enable cell-type specific targeting, nano- previous reviews on the mechanics of cell particles (NPs) are often surface-coated with NP interactions17 and of vesicle wrapping biopolymers or macromolecules, bioconju- NPs.18 In particular, we probe the mechan- gated with targeting ligands that bind spe- ical forces generated at the NPcell inter- cifically to the complementary receptors on face and the kinetics and energetics of the the cell membrane. Armed with drug mol- NPcell interactions. We then describe how ecules and/or diagnostic reporters, the NPs the size, shape, elastic modulus and surface may transport in the bloodstream, adhere to chemistry of NPs affect the interactions and the endothelium, diffuse through the inter- consequently dictate the cellular uptake pro- fi cellular space, speci cally adhere to the dis- perties. The integrated theories presented * Address correspondence to eased cells, enter the cells via different here may form a basis for the rational design [email protected], pathways (Figure 1), and release the drug of NP-based diagnostic and therapeutic [email protected], [email protected]. molecules effectively. Accordingly, the effi- agents with improved targeting efficiency. cacy of NP-based agents depends on the Depending on the particle size and surface Received for review May 26, 2015 efficiency of these subprocesses, many of treatment, engineered particles may enter and accepted August 8, 2015. which remain poorly understood. Instead of cells via different pathways, as schematically Published online giving an exhaustive review on the research shown in Figure 1. Micrometer-sized particles 10.1021/acsnano.5b03184 progress in all the subprocesess, this review can enter the cells through phagocytosis19 or 20,21 sets forth to provide a theoretical foundation macropinocytosis. Phagocytosis (Figure 1a) C XXXX American Chemical Society

ZHANG ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX A www.acsnano.org REVIEW directs the formation of cup-shaped membrane pro- VOCABULARY: Membrane wrapping - the action that trusions that gradually surround and close the parti- cell membrane curves to wrap around an object; Endocy- cles. The shape and size of the phagosomes, i.e., the tosis - the process that cell membrane wraps around an closed membrane protrusions, are dictated by the object and takes it inside the cell; Adhesion Strength - particles being taken up (typically a few micrometers). measures how strong two surfaces cling together; Ligand Phagocytosis is primarily used to uptake dead cells, cell density - refers to the number of ligands per unit area; debris, and pathogens. Macropinocytosis (Figure 1b) is Entropy - a thermodynamical quantity that measures the an actin-regulated process that involves engulfment of disorder of a system; Enthalpy -defined as a thermody- a large quantity of extracellular fluid and particles namic potential that consists of the internal energy of the through plasma membrane ruffling. The membrane system plus the product of pressure and volume of the ruffles exhibit different shapes, and when close, form system; Coarse-grained model - a simulation model that large organelles called macropinosomes.19 Because uses pseudoatoms (coarse grains) to represent groups of of the micrometer length scale of phagocytosis and atoms, instead of explicitly representing every atom in the macropinocytosis, actin assembly plays an imperative system; Molecular dynamics simulation - a computer role in the uptake process.21,22 In clathrin-mediated simulation of physical movements of atoms and mol- endocytosis (Figure 1d), receptorligand binding ecules; Bending energy - the energy stored in an object triggers the recruitment and formation of “coated when it is curved; Deformation - the action or process of pits” (clathrin) on the cytosolic side of the plasma changing in shape of an object through the application of membrane.23 The pits self-assemble into closed poly- force gonal cages that facilitate the endocytosis. Clathrin assembly is also responsible for the formation of vesicle necking and the pinch-off process in the late non-specific interactions as well (Figure 1f). For large stage of membrane wrapping of NPs. Clathrin- NPs, transmembrane penetration may occur provided mediated endocytosis is the most common endocytic the interaction force is sufficiently large.3135 This pathway exploited by viruses.24,25 Caveolin-dependent process, however, may be harmful to cells since large endocytosis (Figure 1c) involves the assembly of the membrane pores must open for particle entry. Small hairpin-like caveolin coats on the cytosolic side of the NPs and molecules (<1 nm) may enter the cell by plasma membrane, forming a flask-shaped caveolae of simply diffusing across the lipid bilayer (Figure 1g). ∼5080 nm in diameter.26,27 It is generally known that With the rapid advance of nanotechnology, NPs Clathrin- and Caveolin-dependent endocytosis in- of different types can now be synthesized with well- volves complex biochemical signaling cascades.28 controlled size uniformity and shape (Table 1), many of However, to what extent the entry of engineered NPs which have manifested a great potential for a broad is regulated by the biochemical signaling remains range of biomedical applications including in vitro/vivo poorly understood. While clathrin and caveolin provide diagnostics,36 cell tracking,37 molecular imaging,3841 additional driving force for endocytosis, clathrin and and drug/gene delivery.4244 These NPs have a common caveolin independent endocytosis29,30 (Figure 1e) can core/coating structure. The cores are either inorganic or also occur through receptorligand binding. NPs with- organic, while the coating layer is generally formed by out conjugated ligands may be endocytosed through natural macromolecules, synthetic biopolymers or their

Figure 1. Possible internalization pathways of NPs.

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entry? Answering similar fundamental questions in TABLE 1. Various Types of NPs as Diagnostic and/or the cellular uptake of synthetic NPs will pave the way Therapeutic Agents toward the development of better principles for the NP type size range typical shapes biomimetic design of highly effective NPs. Metallic 5 500 nm Sphere/cube/rod NPCELL MEMBRANE INTERACTIONS: FORCES Oxides 5200 nm Sphere/cube AND ENERGETICS Quantum dot 230 nm Sphere/ellipsoid Silica 10100 nm Sphere When a NP docks on cell membrane, it forms a highly Carbon nanotube 110 nm Cylinder heterogeneous NPcell interface and initiates dy- Graphene 101000 nm 2D sheet namic physiochemical interactions and a sequence of Polymer 10 1000 nm Spherical/cylindrical/rod-like/elliptical/ kinetic processes. The interaction forces of different cubic/disk-like origins shape the interactions, modify the associated Nanogel 101000 nm Cylinder Liposome 1001000 nm Spherical energy landscapes, and dictate the endocytosis of 55 Bacteria 5005000 nm Rod/spirals/ellipsoid the NPs. Wrapping NPs necessitates curving the cell Dendrimers 1100 nm Spherical membrane and pulling the membrane against mem- Micelles 10100 nm Spherical/rod-like/worm-like/cylindrical/ brane tension to the wrapping site, presenting resis- elliptical tance to endocytosis. All the other forces, including fi Virus 10 300 nm Icosahedral/spherical/ lament/rod electrostatic, van der Waals (vdW), hydrophobic forces, ligandreceptor binding etc., can be lumped together combinations. The coating layer renders NPs water- as the adhesion force that drives endocytosis. The dispersible, prevents aggregation, reduces nonspecific adhesion force can stem from either specific or non- adsorption in biological systems, and provides a plat- specific interactions, or both.56 Specific interactions form for conjugation of targeting ligands or other involve recognition and binding of the ligands coated functional molecules (such as a chelator). The length, on the NP surface to the complementary receptors on charge, hydrophobicity, and flexibility of the coating the cell membrane. Analogous to a molecular key-and- molecules,45 and the overall size, shape, and elastic lock system, ligandreceptor binding enforces target- modulus of the NPs are critical mediators for the in vitro ing specificity of NPs. All the other interactions are and in vivo performance of NPs.41,46,47 nonspecific, which generate an overall attraction or Bioconjugated NPs in many aspects are biomimics of repulsion between molecules and generally affected viruses,30,48,49 which represent the most relevant nano- by ionic strength and pH. scale objects in nature to artificial nanomedicine. Just Specific interactions differ from nonspecific interac- as engineered NPs, viruses are typically of size from tions in at least three distinct features, which have pro- 10 to 300 nm, feature a diverse collection of shapes found implications in the uptake kinetics. First, unlike ranging from icosahedral to spherical to filaments nonspecific interactions in which the driving force to bullet/rod, and are coated with ligands on their is spontaneously in action when a NP docks onto the surfaces. Many viruses, such as HCV50 and influenza,29 cell membrane, specific interaction through ligand enter host cells via protein-mediated endocyto- receptor bindings introduces a time delay: wrapping sis,24,25,51,52 are replicated inside the host cells, and necessitates diffusion of the receptors to the binding exit from the host cells via exocytosis (known as sites, thereby setting a characteristic time scale of budding). While viral entry is a highly active process endocytosis.57,58 Second, much like cleavage fracture involving a set of biochemical signaling, budding,53,54 (or crack healing) in crystals that involves discrete bond in contrast, is largely passive and can be regarded as breaking (or formation),59,60 ligandreceptor binding the reverse process of endocytosis of synthetic NPs. proceeds in a discrete manner. As the chemical energy The high efficiency and specificity of viruses have release (the driving force) is only available after each stimulated enormous research efforts to uncover discrete membrane unit (the area covered by each the physical principles harnessed by the evolutionary ligand) wraps the NP, an energy barrier between two design of viruses, which can conveniently lend to consecutive binding events arises from membrane engineer NPs for disease targeting. For example: How bending and tension.53 The wrapping area and hence fast does viral entry/budding occur? How many repli- the energy barrier in each discrete step can be tailored cated viruses can simultaneously bud out from host by the spacing of the ligands (i.e., the ligand density) cells? Why viral entry/budding is size selective and coated on the NP surface. This barrier further delays shape sensitive? Why are that many ligands needed wrapping, but the relevant time scale is thought to be for viral entry/budding and what if the virus is a few shorter by several orders of magnitude than that of the ligands less or more? Does nature design via evolution receptor diffusion. However, when the coated ligands the number of ligands and the size/shape such that are sparse, the barrier becomes non-negligible. Third, these parameters work in concert for virus infection? receptors, in addition to providing adhesion force, Does local biomechanical environment influence viral also carry translational entropy.6163 Wrapping is thus

ZHANG ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX C www.acsnano.org REVIEW no longer a local event but global in nature as it causes redistributions of the receptors on the entire cell membrane. Concentration of receptors to the NP sur- face through ligandreceptor binding involves entro- pic penalty. The dual character (releases chemical energy upon binding and at the same time carries entropy) renders the adhesion strength in receptor- mediated endocytosis a variable quantity,6366 in dis- tinct contrast to the adhesion strength in nonspecific uptake that is locally defined. Figure 2. Membrane deformation energies when wrapping During wrapping, membrane bends away from its a NP. intrinsically curved state characterized by the sponta- fi neous curvature κ0. The spontaneous curvature arises equilibrium membrane pro le is a catenoid, a minimal from the asymmetry of the lipid bilayers and/or the surface with zero mean curvature. presence of asymmetrically shaped transmembrane Membrane curves locally but gets tensed globally. proteins in general, and the assembly of the protein A characteristic length scale that weighs the relative coats in particular in the case of clathrin and caveolin significance of bending and stretching energies dependent endocytosis. The bending energy density characterizes the locality of an event: λ =(2B/σ)1/2,68 2 σ (per unit area) is quantified by 1/2B(κh κ0) , where B is where is the membrane tension. For typical values of σ fi λ ≈ the membrane bending stiffness, κh =(κ1 þ κ2)/2 is B =15kBT, = 0.05 mN/m, one nds 50 nm. For NP λ the mean curvature of the membrane, and κ1 and κ2 radius R < , bending dominates the wrapping process are the two principal curvatures of the NP surface. and membrane tension is negligible; as R increases To pull the surrounding membranes toward the site from λ, membrane tension effect becomes progres- for wrapping, work against membrane tension needs sively more pronounced. to be done. Cells may actively modulate their mem- ff CELLULAR UPTAKE OF SPHERICAL NPS: SIZE brane tension under di erent physiological conditions EFFECT through various mechanisms, for instance, membrane reservoir release.67 Membrane wrapping first activates When Can a NP be Endocytosed? Given a spherical NP of the release of membrane reservoirs during which radius R, a first question one asks is whether it can be membrane tension remains nearly constant. Once internalized by the cell. We begin with a simple case the excess membrane area is used out, the membrane in which nonspecific adhesion is the only driving force elastically extends to further wrap the NP during which for membrane wrapping. The total adhesion energy η π 2R membrane tension increases. supplied for fully wrapping the NP ( =1)is4 R ns, R The coupling between membrane bending and where ns is the adhesion strength. Assuming a vani- κ stretching in the wrapping process complicates the shing spontaneous curvature ( 0 = 0), the bending calculation of the membrane deformation energy. energy for fully wrapping the NP is C =8πB, indepen- 2 For a partially wrapped NP with a wrapping extent η dent of NP size, and the stretching energy is Γ =4πR σ. (the areal ratio of the wrapped and the total surface Balancing the adhesion energy and membrane defor- area of the NP), the deformation energy consists of mation energy defines a lower limit of the NP radius three contributions: the bending energy C(η) and the below which the NP cannot be endocytosed stretching energy Γ(η) stored in the membrane seg- pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R ¼ 2B=(R σ) (1) ment wrapped onto the NP (the black line segment in min ns Λ η Figure 2), and the additional deformation energy ( ) As Rmin < λ generally holds, the effect of membrane 1/2 (including both bending and stretching) stored in tension is negligible, and Rmin ≈ (2B/Rns) . Consider- the curved membrane detaching from the contact ing a typical value of membrane bending rigidity 68,69 to the NP (the green line segment in Figure 2). B ∼ 15 kBT, and of the nonspecific adhesion strength η ∼ η Γ η ∼ η2 Λ η 2 For spherical NP, C( ) , and ( ) , and ( )is Rns ∼ 1 kBT/nm , Rmin ∼ 5 nm. NPs smaller than Rmin generally a nonlinear function of η. The total mem- may enter the cells by other pathways, such as trans- brane deformation energy at the degree of wrapping location (Figure 1g). It is also possible that several small η (0 e η e 1) is the sum of the three components: NPs may agglomerate into a cluster through mem- W(η)=C(η) þ Γ(η) þ Λ(η). Determining Λ(η) generally brane curvature mediated attraction.70 The agglomer- requires numerically calculating the equilibrium ated NP cluster may well exceed the lower size limit, shapes of the membrane segment,68,69 but becomes and thereby be able to be internalized together.71 One trivial under two special conditions: for a fully wrapped notes from eq 1 when Rns = σ, Rmin f ¥, a condition NP (η = 1), the host membrane sets back to its original under which endocytosis will never occur regardless of curvature at this special stage, and Λ = 0; under the its size because the adhesion energy is fully paid to the tensionless condition, Λ(η)=Γ(η) = 0 for all η since the stretching energy, leaving none to pay the curvature

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Figure 3. (a) Schematic illustration of membrane wrapping of a single NP, driven by ligandreceptor binding. Wrapping depletes the receptors in the near vicinity of the NP, creating a receptor concentration gradient that drives the diffusion of the receptors from the remote region to the binding sites. (b) Interrelated effect of NP size and ligand density on the endocytic time of a NP.66 Reproduced from ref 66. Copyright 2010 American Physical Society. energy. As pointed out previously, the self-regulated is entropically too expensive. The singular con- rest membrane tension by cells is usually small. How- dition implies an upper NP radius (with a fixed ever, with increasing NP size, wrapping the NP would ligand density) beyond which wrapping is source put the membrane in increasingly high tension. (receptor)-limiting. Thus, there also exists an upper limit of NP radius How Fast Can a NP Be Endocytosed? Once a NP exceeds beyond which endocytosis does not occur either.72 the minimal size, endocytosis becomes thermodyna- This upper limit ought to be at the same length scale mically possible. An immediate question that follows of the cell. is the time duration for completing endocytosis. To see In the case that membrane wrapping is primarily this, we note that the wrapping rate is limited by driven by specific interaction, the adhesion strength several barrier-crossing events. As pointed out pre- 64,65 can be partitioned into two components: Rs = viously, an energy barrier arises due to the discreteness

Rh þ Rr, where Rh and Rr are the enthalpic and of ligandreceptor binding. With a detailed calculation entropic components, respectively. The enthaplic com- of the deformation energy landscape of membrane ponent is provided by the ligandreceptor binding, wrapping of a NP at different wrapping extents η,

Rh = μξb,whereμ is the chemical energy release Deserno identified another energy barrier that sepa- upon the binding of a ligandreceptor pair and ξb rates the partially and fully wrapped states, indicating 68,69 is the receptor density bound to the NP surface the transition is nonspontaneous. For typical σ (see Figure 3a). Note that in the case that every values of = 0.05 mN/m, R = 30 nm, and B =20kBT, Δ receptor binds to a ligand on the NP surface (one-to- the barrier can be as high as E =40kBT, which is too high to be thermally crossed. Wrapping can thus be one corresponding binding), ξb reaches its maxi- kinetically trapped at a partially wrapped state. The mum, ξl, the density of ligands coated onto the NP surface. Nonspecificinteractioncanbelumped energy barrier scales with the membrane tension and into enthalpic adhesion strength by adopting an vanishes in the tensionless condition. Increasing the adhesion strength beyond a certain value diminishes effective μeff. The entropic term, Rr, always negative, depends on the local receptor density. A reasonable the barrier as well. When the adhesion strength and the ligand density approximation gives rise to Rr =ln(ξþ/ξl), where ξþ are sufficiently high, the time scales associated with the is the receptor density in the depletion zone near above-mentioned two barrier crossing events are gen- the NP (see Figure 3a). Assuming at the minimal NP erally considered to be shorter than that of receptor radius the number of receptors consumed by wrap- diffusion, and the wrapping rate is predominantly lim- ping is insignificant, causing negligible redistribu- ited by the receptor diffusion. Upon a NP docking on the tion of receptors. One then approximates ξþ ∼ ξ , 0 cell membrane, binding of the receptors to the surface the receptor density at the remote region. Neglect- ligands of the NP depletes the receptors in the vicinity fi ing membrane tension, the energy balance de nes a of the NP, forming a depletion zone with a reduced fi lower limit of the NP radius for the case of speci c receptor density. The concentration gradient of recep- interaction: tors drives diffusion of the receptors from the remote pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ = μξ þ ξ =ξ region to the depletion zone, making subsequent Rmin 2B [ l ln( 0 l)] (2) wrapping possible. To quantify the endocytic time, 57 One notes a singular condition Rh =|Rr|existsunder Gao et al. have developed a front-tracking diffusion which endocytosis is not possible (as Rmin f ¥) model that couples conservation of receptors and because recruiting receptors to wrapping the NP chemical potential balance of the receptors in the

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Figure 4. Simultaneous entry of multiple NPs. (a) Schematics. (b) Phase diagram of cellular uptake in the space of particle size and ligand density. Reproduced from ref 66. Copyright 2010 American Physical Society. depletion zone and on the NP surface. The model et al. further predicts the speed factor for wrapping a predicted that the endocytic time is NP size dependent, as spherical NP:66 ¼ β 2= β ¼ ξ^ξ = ξ ξ tw R D (3) 4 l ( 0 þ ) (5) μ ^ ^ where D is the diffusivity of the receptors, and β is where ξþ = e ξ/(1 ξ). On the basis of eq 5, a phase dimensionless, but dependent on R,referredtoasthe diagram of 1/tw can be constructed in the space of the “speed factor”. The speed factor can be analytically two controlling parameters, NP radius R and ligand fi calculated for cell membrane of in nite size wrapping density ξl, as shown in Figure 3b. One identifies a lower a spherical or a cylindrical NP. With physiologically rele- phase boundary below which tw f ¥ and an upper vant parameters, the model identified an optimal NP size phase boundary beyond which the same limit occurs. of 2730 nm in radius at which the endocytic time is the The lower phase boundary is enthalpically governed, shortest. as defined in eq 1, and the upper phase boundary is The scaling law can also be followed from the entropically governed, as in eq 2. Between these two 57,58,66 conservation of receptors, which defines a char- extreme conditions, there exists an optimal condition acteristic length scale of the impact region L from at which the endocytic time minimizes, corresponding π 2ξ which receptors are depleted for wrapping: L 0 = to the ridgeline in the phase diagram. At the saturated π 2ξ ff 4 R l. For all the receptors to di use and bind to the ligand density, the optimal NP radius for the shortest surface ligands of the NP, the wrapping time is then endocytic time is ∼25 nm, which agrees well with the ∼ 2 ∼ 2ξ ξ tw L /D R l/D 0. This scaling analysis also reveals prediction of the front-tracking diffusion model57 and that the endocytic time correlates positively with previous experimental data.73,74 the ligand density but negatively with the receptor How Many NPs Can Be Taken up by a Cell? Another densities on the cell membrane. problem, equally important to the endocytic time These above analyses assumed that every ligand of a single NP, is the cellular uptake of NPs by cells. binds to a receptor in wrapping the NP, i.e., one-to- The total cellular uptake of NPs matters for a range of one corresponding binding. However, in the case of biomedical applications of NPs, including the maximum densely coated ligands on the NP surface and high drug dosage that can be reached when the NPs are used ffi ligand receptor a nity, wrapping may proceed with for drug delivery, or the signal intensity when the NPs fi some ligands unbound to receptors. This is bene cial are used for intracellular imaging and disease diagnosis. as far as the endocytic time is concerned because fewer When the cell in in vitro experiments is immersed in receptors are required, but detrimental due to the loss culture medium loaded with dispersed NPs of a bulk fi of targeting speci city. A thermodynamic model by density j, the system eventually reaches a steady state Yuan et al. predicts the binding density of the receptors with finite cellular uptake.71,75,76 The steady state can 66 relative to the ligand density on the NP surface be regarded as a thermodynamic equilibrium at which K^ a total of n NPs are associated with the cell. Of the ξ^ ξ =ξ ∼ 1 e (4) b l n NPs, some are wrapped by the cell membrane with ^ 2 63,64 Here, κ=2B/R ξl is the curvature energy in the unit area different degrees of wrapping; some are interna- covered by each ligand. Clearly from eq 4, one-to-one lized, as schematically shown in Figure 4a. The exact corresponding binding (ξ^ = 1) occurs only when the partition of the NPs is driven by the chemical potential unit bending energy κ^ is sufficiently large. For a difference between the NPs that are bound to the cell sufficiently large NP (thus relatively small κ^) but fixed membrane, those suspended in the solution and inter- ^ ligand density ξl, ξ can be significantly smaller than 1. nalized into the cell. The cell membrane is also parti- Under this condition, membrane wrapping may pro- tioned into two parts: a free, planar membrane region ceed with many ligand missed by receptors. Yuan and a curved membrane region bound to the NPs.

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The energetics description of multiple NPmembrane Noticeably, the optimal conditions for the shortest interactions remains nearly the same as in single NP endocytic time (Figure 3b) and highest cellular uptake endocytosis for either nonspecific or specific interac- (Figure 4b), and hence Θ, are similarly close to the 2 tions, with the only added entropics of NP distribution. lower phase boundary: R ξl =2B/μ. Indeed, both the 2 Equating the chemical potential of the NPs in the bulk ridgelines follow a hyperbolic fitting: nopt ≈ 4πR ξl, solution and on the cell membrane gives rise to the where nopt is the optimal number of ligands coated on cellular uptake (the total number of endocytosed NP surface. This is not surprising: once the number NPs):64,65 of ligands coated onto the NP surface exceeds the

π 2 R η ¼ minimal value, the energy balance condition is met. ¼ φ 4 R [ M w( 1)] N A e (6) Coating additional ligands is no longer beneficial, where A is the surface area of the cell accessible by but only increases the number of receptors required for wrapping and thus intensifies the competition the NPs, RM is the adhesion strength and the super- script “M” denotes the case of multiple NP entry, and for receptors among NPs, leading to longer wrapping w(η =1)=2B/R2 þ σ is the membrane deformation time and less cellular uptake. Given the biophysi- energy density (per unit area) at the fully wrapped state cally relevant ranges for membrane bending rigidity μ η =1. (10 40 kBT) and receptor ligand binding energy Figure 4b plots the phase diagram of the cellular (10 20 kBT), the optimal number of ligands nopt uptake in the space of NP radius and ligand density (≈ 8πB/μ) coated onto NPs falls in the range driven by specific interactions. Similar to the phase ∼10100, irrespective of the NP size. The extensively diagram for the endocytic time in Figure 3b, there studied model system, the Semliki Forest virus (SFV), is exists a lower and an upper bound of the cellular about 35 nm in radius, covered with 80 glycoproteins 80,81 uptake, with the enthalpic and entropic origins, re- (ligands), which appears to follow the optimal spectively, as previously discussed. Indeed, one notes condition. from eq 6 that N is small when the adhesion energy is The above energetics analysis suggests that tailor- insufficient to pay the membrane deformation penalty: ing enthalpics and entropics shift the phase bound- aries and modifies the cellular uptake. For sufficiently RM e w(η = 1). This follows essentially the same lower bound dictated by eq 1. Increasing the NP size and/or large NPs, the cortical actin network may play a resist- 82 ligand density intensifies the competition for receptors ing role in endocytosis. This factor may be taken by the NPs,77,78 leading to increasingly high entropic into account by simply defining an effective bending rigidity B ff. Nonspecific interactions, including hydro- cost and thus decreased RM. This entropic limit corre- e sponds to the upper bound defined by eq 2. The phase phobic, electrostatic and van der Waals interactions, diagram also identifies a small region (the red region) may also contribute to additional adhesion energy. within which cellular uptake is maximized. This region Lumping the specific and nonspecific interactions together defines an effective ligandreceptor binding corresponds ∼ R ∈ (25, 30) and ξl ∈ (0.8, 1), with a total μ μ cellular uptake of a couple of thousand for physiologi- energy, eff. A relative variation of both Beff and eff cally relevant parameters. Both the range of the pre- alters the enthalpics and hence the lower bound of 79 dicted total cellular uptake and the optimal range of NP the phase diagrams. On the other hand, increasing 71,74,75 ξ size agree with the experimental data. receptor population (i.e., increasing 0) lowers the The Optimal Condition. From an energetics viewpoint, entropic penalty for the receptors to bind with NPs, multi-NP entry is mechanistically similar to single-NP and hence shifts the upper bound upward. A high j endocytosis. The energy balance of single-NP endocy- bulk density of NPs in solution yields a high surface tosis remains to be met in multi-NP entry, giving rise to concentration of NPs on cell membrane, leading to fi the same enthalpically regulated lower phase boundary. intensi ed competition for receptors among adhering 77,78 Irrespective of a single NP or multi-NPs, wrapping con- NPs and high entropic penalty. This follows that j sumes receptors and is thus source-limiting, leading increasing shifts the upper bound of the uptake rate ff to the same entropically modulated upper phase downward. One further notes that the e ect of mem- fi boundary. It should be pointed out that in the case brane tension is negligible for small NPs but signi cant the NPs in multi-NP entry are spatially too close on the for large NPs. This follows that membrane tension cell membrane such that their membrane curvature- primarily regulates the upper bound of the uptake ff 79 mediated interactions70 are not negligible, the lower rate, but hardly a ects the lower bound. phase boundary may deviate from that of single-NP SHAPE EFFECT endocytosis. Nevertheless, the same mechanisms reg- ulating the phase boundaries for the endocytic time and Nonspherically shaped NPs are also widely used in cellular uptake allow us to define a nominal cellular biomedical diagnostics and therapeutics. Their poten- uptake rate,79 as tial nanotoxicities have also attracted much attention. Typical 1D nanomaterials include nanotubes, nano- Θ ; ξ ¼ = (R l) N tw (7) wires, and filamentous bacteria with radius at the

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in their level of details, depending on the number of agents per lipid and complexity of the inter-agent interactions. Early CG models for lipid bilayers used explicit solvents that are also coarse-grained. As the solvent occupies a 3D volume, the associated degrees of freedom outnumber those of the 2D lipid bilayers, and the majority of the computational cost goes to the solvent, rather than the lipid bilayer. Thus, CG models with implicit solvent are particularly attractive. Stabiliz- Figure 5. Simulation models of lipids at different length ing the coarse-grained lipid bilayer in a 2D fluid phase scale. (a) All-atom model of the DMPC lipid molecules; (b and c) CG models, a 10-agent92 (b) and a 3-agent93,94 (c) and under solvent-free condition with physiologically CG model; and a one-agent-thick membrane model95 (d). relevant membrane properties was numerically non- 89,90 (e) Triangulated membrane model. trivial. Varying such solvent-free CG models need to use complicated multibody potentials to achieve bio- nanoscale but length at a much larger scale; typical physically relevant membrane properties. Solvent-free 2D nanomaterials are plate-like materials with thick- CG models with simple pairwise potentials have only ness at the nanoscale but lateral dimensions at a much been recently developed; of particularly noteworthy larger scale, including mica nanosheets, boron nitride are the 3-bead model by Cooke et al.93,94 and the one- nanosheets, and graphene-family nanomaterials, as agent-thick model by Yuan et al.95 These models are listed in Table 1. For 3D nonspherical NPs, their three computationally highly efficient while biophysically dimensions are comparable. For all these nonspherical faithful to the underlying molecular interactions in a nanomaterials, the fundamental biophysics of cellNP wide range of membrane-mediated processes, includ- interactions established for spherical NPs remains ing endocytosis. valid. However, owing to their asymmetrical geo- The one-agent-thick lipid bilayer model95 metries, they exhibit unique wrapping modes during (Figure 5d) coarse-grains the lipid membrane as a endocytosis.83 88 single layer of agents that are self-assembled into Coarse-Grained Models. The energetics of endocytosis a2Dfluid surface in a solvent-free environment. The of a nonspherical NP is complicated by the symmetry inter-agent interaction potential is anisotropic but breaking of cell membrane deformation morphology, of a pairwise form, composed of two functions that for which the deformation energy is analytically non- separately control the distance and orientation depen- trivial, particularly when membrane tension is non- dence. The model membrane properties are highly negligible. To investigate the effects of NP shape on tunable through only four key model parameters that the kinetics of endocytosis, computational modeling at control separately the lipid diffusivity, bending and different length scales provides a powerful alternative. area compression moduli, and spontaneous curvature, Since the length and time scales involved in NP respectively. The simple interaction potential can lead endocytosis are on the order of 100 nm or more, and to robust self-assembly of randomly distributed agents milliseconds to minutes, respectively, they are typically in 3D space into 2D fluid membranes. Through careful beyond the reach of the full-atom molecular dynamic mapping to the membrane bending modulus and the (MD) simulations (Figure 5a). To the other end of the in-plane lipid diffusivity, the in-plane agent dimension length spectrum, the triangulated membrane simula- of our model is found to be ∼0.5 nm and the basic tion models89,90 (Figure 5e) spatially discretize mem- time scale of our model is ∼0.1 μs. Both the length and brane into triangles in the general framework of time scales are at least one order of magnitude higher Helfrich theory.91 However, these continuum models than other solvent-free CG models.92,99,100 The model suffer from additional numerical burden in addressing was successfully applied to study homogeneous vesi- lateral diffusion of lipids and receptors, which is the key cle shape transformation under osmotic conditions,101 factor dictating the time scale of endocytosis. protein-mediated lipid sorting and domain coarsen- To gain a molecular-scale understanding of NP ing of ternary membranes,102 and red blood cell targeting, it is essential to develop multiscale models disorders.103,104 that link interactions on the molecular level and NP Simultaneous Rotation and Wrapping of 3D Nonspherical absorption/uptake by the cells at the subcellular level. NPs. Huang et al.83 adopted the one-agent-thick Coarse-grained (CG) methods92100 (Figure 5bd) membrane model to characterize the endocytic mode have gained popularity for their flexibility and diversity. of spherocylindrical NPs with different aspect ratios. In CG models typically involve grouping a cluster of this model, NP surface is also coarse-grained to discrete atoms into a single CG agent, thereby reducing the agents, some representing ligands (see Figure 6ac). total number of the degrees of freedom by several The lipid membrane is made to be tensionless by orders of magnitude, and accordingly improving the scaling the membrane area in the CGMD simulations. computational affordability. Such CG approaches vary The aspect ratio of the spherocylindrical NPs is defined

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Figure 6. (ac) Simulation snapshots of the endocytic process of spherocylindrical NPs with different aspect ratios. For all the cases shown, R = 14 nm. (a) F = 1; (b) F = 1.5; (c) F = 2. Here, τ is a characteristic time scale of the model. Color-coded beads represent different coarse-grained constituents. Green, lipids; blue, receptors; yellow, ambient NP surface; red, ligands. (d). Shape effects on the endocytic time of NPs. Evolution of the areal wrapping fraction of NPs with the same radius (R = 10.0σ) but different aspect ratios. In the simulations, the spherocylindrical NPs are initially docked on the membrane with their long axes perpendicular to the membrane. Reprinted from ref 83. Copyright 2013 American Chemical Society. by F =(R þ 0.5L)/R, where R and L are the radius of the to increasing endocytic time, obeying the scaling law. hemispherical caps at both ends and the length of the This nonmonotonic behavior may be due to the dis- cylindrical portion, respectively. In the simulations, the tinct entry modes from spherical to spherocylindrical spherocylindrical NPs are initially docked on the pre- shape transitions. The scaling law and the simulation equilibrated membrane, with their long axes normal to results indicate frustrated uptake of NPs with very high the membrane surface (θ =90). Figure 6ac depicts aspect ratios, such as 1D nanorods. the snapshots of the endocytic process of the NPs with The wrapping energy landscape explains the se- three different aspect ratios, F = 1, 1.5, and 2. Note F =1 quence of simultaneous membrane wrapping and represents a spherical NP. All the three NPs can be rotation during the internalization of a spherocylind- completely endocytosed through a general process rical NP. Figure 7a plots the curvature energy profiles involving membrane invagination, membrane necking for the NP (F = 2) as a function of the wrapping extent η, and pinch-off. as if the NP were wrapped with a fixed entry angle, Distinct entry modes are observed in the wrapping θ =0 (horizontally) or θ =90 (vertically). The analy- process of the spherocylindrical NPs, as shown in tical energy profiles, denoted by solid lines, agree very Figure 6ac. For F = 1, wrapping is accompanied by well with the CGMD simulations, denoted by symbols. NP rotation. For F = 1.5, the NP tilts by an angle of ∼20 For horizontal wrapping (θ =0) the curvature from its initial upright docking position once wrapping energy linearly scales with the wrapped areal fraction. begins. Membrane wrapping of the NP then proceeds For vertical wrapping (θ =90), the energy profile is at this angle until the NP is fully internalized. The constituted of three linear curves with different slopes. invagination of the NP with a larger aspect ratio (F =2) Since the two wrapping angles represent the extremes, involves two symmetry-breaking processes. At the initial the curvature energy profiles of all the other wrapping wrapping stage, the NP rotates until it completely lays angles are enveloped by these two curves. The energy down on the membrane surface with its long axis. The NP profiles indicate the sequence of membrane wrapping then stands up and is finally endocytosed with a nearly and NP rotation. At a small wrapping extent (η < 0.5), 90 entry angle. Such a lying-down-then-standing-up the relatively smaller curvature energy for θ =0 sequence appears to be universal for spherocylindrical suggests that an initially vertically docked or titled NPs with F > 2. If the initial docking angle θ =0 with the (0 < θ <90) NP would tend to lay down by rotation, long axis parallel to the membrane surface, the NP would i.e., aligning its long axis with the membrane surface. simply stand up and then be endocytosed. Once η > 0.5, the NP would tend to stand up to gain a At prescribed ligand density and NP radius and larger wrapping angle θ since wrapping with a large assuming one-to-one corresponding binding of angle involves a smaller energy penalty. Upon comple- ligandreceptor pairs, the endocytic time is propor- tion of rotation, the NP would be wrapped with this tional to the total number of receptors required for angle until it is completely endocytosed. Thus, an initially fully wrapping the NP. One then follows the scaling vertically docked NP would take a laying-down-then- law: tw ∼ F. However, from the CGMD simulations by standing-up sequence to complete endocytosis, as Huang et al.,83 the spherical NP takes longer time to be schematically shown in Figure 7b. fully endocytosed than the spherocylindrical NP of F = The laying-down-then-standing-up wrapping se- 1.5, but shorter time than the spherocylindrical NP of quence is consistent with the CGMD simulations for F = 2, as shown in Figure 6d. Further increasing F leads capped multiwalled carbon nanotubes (MWCNTs) by

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Figure 7. (a) The bending energy profile for internalizing a spherocylindrical NP (F = 2) with different wrapping angles explains the laying-down-then-standing-up process. (red: θ =0; black: θ =90.). (b) Schematics of the laying-down-to- standing-up process. Images reprinted or adapted from ref 83. Copyright 2013 American Chemical Society.

Figure 8. (a) Two modes of interaction between a cell membrane and a nanotube.88 Reproduced from ref 88. Copyright 2014 American Chemical Society. (b) Elastic energy change as a function of the normalized membrane tension σh, where σhc =2π/5 is the critical point of transition between these two interaction modes.

Shi et al.84 using the 3-agent lipid model and the exhibits a lying-down-then-standing-up sequence as accompanying experimental observations. A very long identified in Figures 6 and 7, recent work has revealed capped CNT can be considered as a 1D rod, the limiting two fundamental modes of interaction between a 1D geometry of the spherocylindrical NPs. The simulations nanomaterial and the cell membrane: a perpendicu- demonstrated that at a relatively low receptor density lar entry mode and a parallel adhering mode (see the CNT rotates and is internalized with an entry angle Figure 8a).88 Theoretical analysis showed that these close to 90, exhibiting a tip-entry phenomenon. Also two basic modes are controlled by a single dimension- consistent to the analysis in Figure 7a, the rotation is less parameter, the normalized membrane tension σh = driven by the relaxation of the deformation energy in 2σR2/B with R being the radius of the 1D nanomaterial. the membrane during wrapping. From an energetic point of view, σh represents the The tip rotation from a kinetics point of view by relative ratio of the membrane stretching and bending noting two relative time scales involved in the endo- energies in the total elastic energy of the membrane. cytosis of the CNTs, as pointed out by Shi et al.:84 the The membrane bending energy tends to rotate the wrapping time controlled by receptor diffusion and the nanotube to a perpendicular entry angle while the NP rotation time controlled by the torsional force. In membrane stretching energy prefers a vanishingly the case of physiologically relevant receptor density, small entry angle. When σh falls below a critical value wrapping is the limiting process compared to rotation. σhc (σh < σhc), the membrane bending energy dominates Thus, the NP has sufficient time to rotate so as to fully over the stretching energy and the 1D nanomaterial relax the deformation energy to achieve tip entry. On rotates to a high entry angle during uptake. For σh > σhc, the contrary, in the case of very high receptor density, the 1D nanomaterial is driven by the dominating receptors are always immediately available for wrap- stretching energy toward a low entry angle and even- ping and wrapping would proceed very fast, leaving tually adheres to the membrane surface in a near- no time for rotation to occur. Under this condition, the parallel configuration (see Figure 8b). This σh-governed NP is endocytosed with a low entry angle and tip entry uptake behavior is ubiquitous in the interactions be- becomes less predominant.105 tween 1D nanomaterials and cell membranes, and the Uptake of 1D and 2D Nanomaterials. Compared with the theory can be employed to understand many biologi- endocytosis of 3D nanorods whose interaction mode cal phenomena such as the regulation of filopodia

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Figure 9. (a) Schematic of typical wrapping states and (b and c) wrapping phase diagrams with respect to normalized adhesion energy and membrane tension σh at different values of the rigidity ratio BL/B, where BL is the bending rigidity of the liposome; (b) 2D case; (c) 3D case. Dashed lines, boundaries between no wrapping and partial wrapping states; solid lines, boundaries between partial and full wrapping states. Adapted with permission from ref 106. Copyright 2011 American Physical Society. radius and the instability of microtubules confined by UPTAKE OF SOFT NPS 88 cell membranes. For soft NPs with comparable bending modulus as The reason why the receptor-mediated endocytosis the lipid bilayer, such as vesicles, liposomes, micelles, of nanorods exhibit a single interaction mode of a polymeric capsules, and NPs coated with long poly- lying-down-then-standing-up sequence (Figure 7), mers, both the cell membrane and the NP itself deform. while that of 1D nanomaterials exhibits two interaction The partition of the total deformation energy into the σ modes depending on the scaled membrane tension h cell membrane and the NP alters the energy landscape, could be understood as follows. Note that receptor- giving rise to different kinetics of endocytosis. During mediated endocytosis is usually regarded as a process the wrapping process, the NP deforms into different ff limited by the di usion of receptors in the cell mem- shapes, thus the effect of elastic modulus is inherently 57 brane toward the contact region. The membrane coupled with the shape effect. wrapping of the curved tip of a 1D nanomaterial is Yi et al.106 developed a theoretical model concern- ff governed by 2D di usion of receptors in the membrane ing the endocytosis of a fluid vesicular NP such as a lipo- plane, while the wrapping of the cylindrical wall is some in the framework of Helfrich theory. By solving ff regulated by 1D di usion of receptors. This means that the equilibrium shape equations of the cell membrane the tip, rather than the lateral wall, of a 1D nanomaterial as well as the vesicular NP, the total deformation energy should be wrapped first. As long as the specific energy of the system can be obtained at different wrapping of receptorligand interaction can overcome the mem- extents (see Figure 9a). Their energetics analyses brane deformation energy penalty induced by the tip showed that endocytosis is very sensitive to the relative wrapping, the subsequent interaction should be con- stiffness of the NP to the cell membrane, as shown in trolled by the two tension-dependent interaction the phase diagram of the scaled membrane tension modes.88 In comparison, for short nanorods with two σh and adhesion energy density R =2RR2/B, where R is curved tips and a much smaller lateral wall, the differ- the adhesion energy density (see Figure 9b,c). As NP ence between receptor diffusion between the tip and becomes softer, the transition lines separating from wall regions is not as evident. Therefore, the wrapping of short nanorods would be mainly governed by the partial to fully wrapping shift downward, indicating ffi elastic energy of the deformed membrane that adopts endocytosis is more di cult to complete. The result ff the lying-down-then-standing-up sequence to reduce that sti vesicular NPs can achieve full wrapping more fi the membrane deformation energy. easily than soft NPs has been con rmed recently in a Depending on their size, geometry and surface pro- combination of experiments and molecular dynamics perties, 2D nanomaterials can exhibit several different simulations on the cell uptake of coreshell NPs with 107 configurations in the cellular interaction.85 Recently, a lipid shell. Similar elasticity effects have also been a theoretical analysis has been performed to study observed in the cell uptake of spherical solid nano- two modes of interaction between the cell membrane capsules108 and (2D cylindrical) nanorods. It was found and a rigid 2D nanomaterial: near-perpendicular trans- that solid nanocapsules require less adhesion energy to membrane penetration and parallel attachment onto achieve full wrapping than fluid vesicular NPs with the a membrane. It was shown that the splay (bending) same bending stiffness.108 and membrane tension energies serve as the main To explain why softer NP is more difficult to be endo- driving force for the near-perpendicular (parallel) con- cytosed, one observes that cell membrane wets soft figuration of a transmembrane (membrane attaching) NPs once they dock on the cell membrane, as shown in 2D nanomaterial.87 As 2D nanomaterials enter the Figure 9a. The softer the NP is, the larger the wetting cells typically not via endocytosis but other pathways, angle, and the higher extent of spreading of the NP on their internalization mechanisms are not detailed the cell membrane. The highly spread NP forms large here. curvatures at the spreading front. Further wrapping the

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Figure 10. Left: Cellular uptake of the fluorescent NPs by the cells on polyacrylamide substrates of varying stiffness. Cells were cultured on substrates for 12 h before loading the NPs. Images were taken after loading the NPs for 6 h. Right: The total fluorescence yield of individual cells on the polyacrylamide substrates of varying stiffness obtained by multiplying fluorescence per unit area by the projected cell area on a cell by cell basis.117 The difference between any two groups at any specified time point of measurement is statistically significant (p < 0.01 using Student t test). Reproduced from ref 117. Copyright 2013 American Chemical Society.

NP involves overcoming a very large bending energy of cell culture substrates. In a first study, polyacryla- barrier inherent to the spread shape. The energy mide (PA) hydrogels of varying stiffnesses, soft barrier may be sufficiently large to completely stall (Young's modulus: 1.61 ( 0.11 kPa), intermediate the wrapping. Interestingly, Yi et al.106 noted that many (3.81 ( 0.12 kPa), and stiff (5.71 ( 0.51 kPa) were used viruses exploit the stiffness to facilitate the infectious in the in vitro experiments to explore the effect of process: they soften before uptake via fusion, while substrate stiffness on the cellular uptake.117 Bovine harden before budding out of the host cells via aortic endothelial cells (BAECs) were cultured on the exocytosis. gels for 12 h before loading fluorescent polystyrene NPs (100 nm) into the culture medium. The seemingly LOCAL MECHANICAL ENVIRONMENTAL EFFECTS small difference in the gel stiffness is sufficient to Our previous analyses reveal that cellular uptake of induce changes in cell morphology, as shown by the NPs depends on not only the size, shape and chemo- phase contrast images (Figure 10, left). Endocytosis physical properties of NPs, but also the biomechanical was driven by nonspecific interactions, since the properties of cell membrane, including membrane NPs are not conjugated with antibodies. The in vitro tension and bending modulus. In parallel to the theo- experiments confirmed that substrate stiffness plays a retical and computational studies, numerous in vitro significant role in altering the cellular uptake of NPs. experiments71,75,109,110 have been carried out to assess The total fluorescence yield per cell was measured at the delivery efficiency of NPs and provided rich data different times after NPs were loaded, indicating the sets for validating the theoretical and computational uptake level of NPs. With increasing substrate stiffness, models. However, in these in vitro experiments the the cellular uptake per cell increases (Figure 10, right), cells were exclusively cultured on glass or plastic but the cellular uptake per cell surface area decreases substrates, which are both mechanically stiff and topo- (not shown here).117 graphically flat. In contrast, the ECMs in vivo are soft Using poly(methyl methacrylate) (PMMA) fibrous sub- and consist of fibrils such as collagens. These dis- strates fabricated via electrospinning, Huang et al.118 crepancies raise an immediate concern regarding to further explored the effects of substrate topography, what extent the in vitro experimental results are trans- characterized by the fibril density, on the cellular uptake ferrable to in vivo conditions. It has well established of NPs. Substrates of three types of topographies, flat from the study of mechanobiology111116 that local PMMA surface, and sparse and dense PMMA fibrous physical cues of various kinds modulate cell responses, substrates, were used. The responses of human osteo- resulting in changes in cell morphology and surface sarcoma SaOS-2 cells to substrate topography were mechanics, which may in turn affect the cellular uptake investigated using fluorescence microscopy by simul- of NPs. taneously staining F-actin, vinculin, and cell nuclei, To characterize the role of local physical environ- as shown in Figure 11 (left). The 100 nm fluorescent ment on the cellular uptake of NPs, Huang et al.117 polystyrene NPs were again used to assess the cellular carried out in vitro studies with different characteristics uptake. Figure 11 (right) shows that the cellular uptake

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Figure 11. Left: Representative fluorescence images of SaOS-2 cells on various substrates with distinct surface topographies. Right: Cellular uptake of fluorescent NPs by cells on substrates of different surface topographies. The fluorescence intensities are normalized by the intensity on flat PMMA surface.118 **Significance at p < 0.01 between any two groups. Reproduced with permission from ref 118. Copyright 2015 Wiley & Sons, Inc. of NPs on sparse fibrous substrates was reduced by For cells on fibrous substrates, the higher membrane about 30% as compared with the cells on the flat PMMA tension renders lower cellular uptake by cells on sparse substrates. fibrous substrate than on dense fibrous substrate. The regulative role of substrate stiffness and topo- CONCLUSION AND PROSPECTIVE OUTCOME graphy on the cellular uptake stems from the altered mechanical properties of cell membrane and the cell The NPcell interface is highly heterogeneous, gen- spreading area, as indicated by eq 6. First, substrate erating forces of different origins that shape the energy stiffness modulates the mechanical properties of cell landscape of NPcell interactions. These forces are membrane. Recent MD simulation results suggested determined by a suite of variables inherent to the NPs that the fluorescence lifetime of DiI chromophores and the cells (size, shape, stiffness, surface chemistry of embedded in lipid bilayer is an effective indicator of the NPs, elasticity of the cell membrane, and receptor relative membrane tension,119 which was confirmed diffusivity, etc.), rendering cellular uptake NP size in experiments.120 Indeed, fluorescence lifetime mea- selective, shape sensitive, and stiffness dependent. As surements of DiI-C12 within cells demonstrated that cell morphologies and surface mechanics are depen- cell membrane is less tense on softer PA gels.117 This dent on the local microenvironment and disease states, predicts that the cellular uptake of cells on softer PA gels cellular uptake of NPs may not only be cell type specific, or denser fibrous substrates is higher on a per mem- but also tissue-environment and disease state specific. brane area basis. Second, substrate stiffness modulates It is clear that the effects of key parameters impor- cell spreading. The stiffer the substrate is, the larger tant to the cellular uptake are strongly interrelated, the spreading area of the cell.117 As shown in eq 6, the as exemplified by the phase diagrams in the space of cellular uptake linearly scales with the surface area of the NP radius and ligand density. The interrelated effects cell membrane, since it represents the assessable area to define a narrow window in the parametric space within the NPs. It turns out that the cell surface area is dominant which the cellular uptake is optimized. In addition to factor over the membrane tension effect, and hence, the the interplay between NP size and ligand density, cellular uptake on a per cell basis increases with increas- many other interrelated effects are yet to be quantified. ing substrates stiffness. For example, when a soft NP is being wrapped, its shape The observed effect of substrate topography on the dynamically changes, i.e., the effects of NP stiffness and cellular uptake can be explained by the same principle. shape are coupled and interrelated. The interrelated

First, fluorescence lifetime measurements of DiI-C12 effects indicate that improving one parameter may showed that cell membrane on sparse fibrous substrate adversely impact another, making the search of is more tensed than those on flat and dense fibrous the optimal parametric window experimentally cost- substrates; membrane tension of cells on the latter two ineffective. Coarse-grained modeling discussed here substrates is comparable.118 The spreading area of will continue to be a powerful tool to define the cells on flat substrate is nearly 2-fold higher than that complex interrelations. of cells on fibrous substrates, whereas the spreading Challenges remain to identify the most efficient areas of the cells on dense and sparse fibrous substrates targeting strategy suitable and specific to diseased are comparable.118 Since the cell surface area is the tissues. Chemotargeting is currently the most popular dominant factor over the membrane tension effect, targeting strategy, wherein NPs conjugated with the cellular uptake on flat substrate is the highest. ligands target cell surface receptors that are specific

ZHANG ET AL. VOL. XXX ’ NO. XX ’ 000–000 ’ XXXX M www.acsnano.org REVIEW to the diseased cells. Such an active targeting method Acknowledgment. S.L.Z. gratefully acknowledges supports has been proven efficient so long as unique receptors from the National Science Foundation (NSF) grants (Career fi Award: CMMI-0754463/0644599; CBET-1067523) and the Na- can be identi ed and are overexpressed on diseased tional Institutes of Health (NHLBI R21 HL122902). H.J.G. acknowl- cells compared with normal cells. The work reviewed edges supports from NSF (CMMI-1028530 and CBET-1344097). here provide compelling evidence that mechanical G.B. acknowledges supports from the National Institutes of Health as an NHLBI Program of Excellence in Nanotechnology properties of the cells and the NPs can also bias the Award (HHSN268201000043C to G.B.) and an NIH Nanomedicine cellular uptake of NPs, which suggests a new targeting Development Center Award (PN2EY018244 to G.B.). We are also strategy, mechanotargeting. Given that mechanical grateful to Mr. Peng Zhao at Penn State University for producing a few images of endocytosis in this manuscript. properties of many tumors are different than those of the normal tissues, mechanotargeting is complemen- tary to chemotargeting and may be useful in achieving REFERENCES AND NOTES more effective cancer diagnosis and treatment. This 1. Liu, X.; Dai, Q.; Austin, L.; Coutts, J.; Knowles, G.; Zou, J.; Chen, H.; Huo, Q. A One-Step Homogeneous Immunoassay opens up a new paradigm for the design of NP-based for Cancer Biomarker Detection Using Gold Nanoparticle nanomedicine with improved targeting selectivity and Probes Coupled with Dynamic Light Scattering. J. Am. reduced toxicity. Chem. Soc. 2008, 130,2780–2782. 2. Mani, V.; Chikkaveeraiah, B. V.; Patel, V.; Gutkind, J. S.; To facilitate a unifying understanding, this review Rusling, J. F. 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